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Application of Intuitionistic Z-Numbers in Supplier Selection

Nik Muhammad Farhan Hakim Nik Badrul Alam1,2, Ku Muhammad Naim Ku Khalif1,*, Nor Izzati Jaini1

1 Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Gambang, Kuantan, 26300, Pahang, Malaysia
2 Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang, Jengka Campus, Bandar Tun Abdul Razak Jengka, 26400, Pahang, Malaysia

* Corresponding Author: Ku Muhammad Naim Ku Khalif. Email: email

Intelligent Automation & Soft Computing 2023, 35(1), 47-61.


Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems. A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives. The proposed model is then implemented in a supplier selection problem. The obtained ranking is compared to the existing models based on Z-numbers. The results show that the ranking order is slightly different from the existing models. Sensitivity analysis is performed to validate the obtained ranking. The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80% to 100% consistency despite the drastic change of criteria weights. Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’ opinions in solving decision-making problems.


Cite This Article

APA Style
Alam, N.M.F.H.N.B., Khalif, K.M.N.K., Jaini, N.I. (2023). Application of intuitionistic z-numbers in supplier selection. Intelligent Automation & Soft Computing, 35(1), 47-61.
Vancouver Style
Alam NMFHNB, Khalif KMNK, Jaini NI. Application of intuitionistic z-numbers in supplier selection. Intell Automat Soft Comput . 2023;35(1):47-61
IEEE Style
N.M.F.H.N.B. Alam, K.M.N.K. Khalif, and N.I. Jaini "Application of Intuitionistic Z-Numbers in Supplier Selection," Intell. Automat. Soft Comput. , vol. 35, no. 1, pp. 47-61. 2023.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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